Which of the following tables shows that y=kf(x) results in the parent function y=|x+4| being vertically stretched by a k factor of 3?(1 point)

To determine which table shows that \( y = kf(x) \) results in the parent function \( y = |x+4| \) being vertically stretched by a factor of \( k = 3 \), we need to evaluate the original function \( f(x) = |x + 4| \) and then see how it changes when we apply the stretch.

1. Calculate \( f(x) = |x + 4| \) for the values of \( x \):
- For \( x = 0 \): \( f(0) = |0 + 4| = 4 \)
- For \( x = 1 \): \( f(1) = |1 + 4| = 5 \)
- For \( x = 2 \): \( f(2) = |2 + 4| = 6 \)

The points for the original function are:
- \( (0, 4) \)
- \( (1, 5) \)
- \( (2, 6) \)

2. Now, applying the vertical stretch by a factor of \( k = 3 \):
- For \( x = 0 \): \( y = 3f(0) = 3 \times 4 = 12 \)
- For \( x = 1 \): \( y = 3f(1) = 3 \times 5 = 15 \)
- For \( x = 2 \): \( y = 3f(2) = 3 \times 6 = 18 \)

Thus, the resulting values when applying the vertical stretch are:
- \( (0, 12) \)
- \( (1, 15) \)
- \( (2, 18) \)

**The correct table is:**

\( x \) | \( y = kf(x) \)
---|---
0 | 12
1 | 15
2 | 18

This shows the function being vertically stretched by a factor of 3. Therefore, the first option is the correct answer.